2 CHAPTER Estimation and Number Theory Lesson 2.1 Estimation Find each sum or difference. Then use rounding or front-end estimation to check that your answers are reasonable. 1. 649 385 Estimated sum: 2. 2,264 8,721 Estimated sum: 3. 538 269 Estimated difference: 4. 18,460 485 Estimated difference: Find each product. Then use rounding or front-end estimation to check that your answers are reasonable. 5. 282 3 Estimated product: 6. 119 5 Estimated product: 7. 188 4 Estimated product: Extra Practice 4A 13
Find each quotient. Then use related multiplication facts to check that your answers are reasonable. 8. 76 4 Estimated quotient: 9. 98 2 Estimated quotient: 10. 87 3 Estimated quotient: Solve. Decide whether to find an estimate or an exact answer. 11. Mr. Jackson has $8,000. He wants to buy the following items. microwave toaster oven coffee machine Complete the table. Item Actual Cost microwave $ $ toaster $ $ oven $ $ coffee machine $ $ Rounded to the Nearest Hundred Does Mr. Jackson have enough money to pay for all the items? 14 Chapter 2 Lesson 2.1
Lesson 2.2 Factors Answer each question. Write Yes or No. 1. Is 6 a factor of 72? 2. Is 8 a factor of 84? 3. Is 7 a factor of 98? 4. Is 4 a factor of 98? 5. Is 9 a factor of 108? 6. Is 5 a factor of 125? 7. Is 7 a factor of 86? 8. Is 6 a factor of 96? Find the common factors of each number pair. Then find the greatest factor. 36 60 9. The factors of 36 are. 10. The factors of 60 are. 11. The common factors of 36 and 60 are. 12. The greatest common factor of 36 and 60 is. 84 72 13. The factors of 84 are. 14. The factors of 72 are. 15. The common factors of 84 and 72 are. 16. The greatest common factor of 84 and 72 is. Extra Practice 4A 15
Look at the numbers. Fill in the blanks. 24 30 45 27 18 50 17. Write all the numbers that have 3 as a factor. 18. Write all the numbers that have 6 as a factor. 19. Write all the numbers that have 3 and 6 as factors. Complete. Find the prime and composite numbers. 9 15 19 26 33 37 45 47 20. The prime numbers are. 21. The composite numbers are. Find the prime and composite numbers in each set. 22. Write the next six prime numbers after 10. 23. Write all the composite numbers between 20 and 30. 16 Chapter 2 Lesson 2.2
Lesson 2.3 Multiples Fill in the blanks. 1. The fi fth multiple of 8 is. 2. The eighth multiple of 9 is. 3. The twelfth multiple of 6 is. 4. The eleventh multiple of 7 is. 5. The seventh multiple of 10 is. Find the common multiples of each pair of numbers. Then find the least common multiple. 4 and 9 6. The fi rst 18 multiples of 4 are. 7. The fi rst 8 multiples of 9 are. 8. The fi rst two common multiples of 4 and 9 are. 9. The least common multiple of 4 and 9 is. 6 and 8 10. The fi rst 8 multiples of 6 are. 11. The fi rst 8 multiples of 8 are. 12. The fi rst two common multiples of 6 and 8 are. 13. The least common multiple of 6 and 8 is. Extra Practice 4A 17
Find the least common multiple of each pair of numbers. 14. 7 and 8 15. 9 and 12 16. 10 and 12 17. 15 and 20 Use these numbers to fill in the blanks. 54 20 48 60 72 18. Write all the numbers that are multiples of 4. 19. Write all the numbers that are multiples of 8. 20. Write all the numbers that are multiples of 9. 21. Find the number that is the least common multiple of 4, 8, and 9. 18 Chapter 2 Lesson 2.3
Put on Your Thinking Cap! Solve. 1. A number is between 10 and 20. It is also a factor of 24. What is the number? 2. It is a 3-digit number. All the digits are different. The fi rst and second digits are multiples of 3. The fi rst digit is greater than the second digit. The sum of the fi rst two digits is 7 more than the third digit. The number is not a multiple of 5. The third digit is greater than 3. What is the number? 3. Jane s age is a two-digit multiple of 4. Next year, her age will be a multiple of 5. How old is Jane now? Extra Practice 4A 19
Solve. 4. Mrs. Garcia watches 16 students cycle home after school. She counts 38 wheels. Some of the students are on bicycles, and the rest are on tricycles. How many students are on bicycles? 5. Michelle has less than 50 baseball cards. If she puts them in packs of 7, she has 5 baseball cards left. If she puts them in packs of 9, she has 6 baseball cards left. How many baseball cards does Michelle have? 20 Chapter 2 Put on Your Thinking Cap!
6. Susan s birthday is in January. The date has two digits. You say the date when you count by fours. The date is divisible by 6. The sum of the digits is 3. When is Susan s birthday? 7. Nathan s birthday is also in January. The date has two digits. The date can only be divided by 1 and by itself. The sum of the digits is 8. When is Nathan s birthday? Extra Practice 4A 21
8. Daniel has won $20 worth of prizes. He can choose from these prizes. Show the ways in which he can select $20 worth of prizes. Use to show the number of each prize he can choose. Adventure Books ($4) Soft Toys ($6) Games ($8) 22 Chapter 2 Put on Your Thinking Cap!